Algebra Examples

$(\frac{4}{5} m^{4} n^{6}) (\frac{3}{2} m n^{2})$

Step 1

Multiply $m^{4}$ by $m$ by adding the exponents.

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Step 1.1

Move $m$ .

$\frac{4}{5} \cdot (m \cdot m^{4} n^{6}) (\frac{3}{2} \cdot (n^{2}))$

Step 1.2

Multiply $m$ by $m^{4}$ .

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Step 1.2.1

Raise $m$ to the power of $1$ .

$\frac{4}{5} \cdot (m^{1} m^{4} n^{6}) (\frac{3}{2} \cdot (n^{2}))$

Step 1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{5} \cdot (m^{1 + 4} n^{6}) (\frac{3}{2} \cdot (n^{2}))$

Step 1.3

Add $1$ and $4$ .

$\frac{4}{5} \cdot (m^{5} n^{6}) (\frac{3}{2} \cdot (n^{2}))$

Step 2

Multiply $n^{6}$ by $n^{2}$ by adding the exponents.

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Step 2.1

Move $n^{2}$ .

$\frac{4}{5} \cdot (m^{5} (n^{2} n^{6})) \frac{3}{2}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{5} \cdot (m^{5} n^{2 + 6}) \frac{3}{2}$

Step 2.3

Add $2$ and $6$ .

$\frac{4}{5} \cdot (m^{5} n^{8}) \frac{3}{2}$

Step 3

Multiply $\frac{4}{5} (m^{5} n^{8})$ .

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Step 3.1

Combine $m^{5}$ and $\frac{4}{5}$ .

$\frac{m^{5} \cdot 4}{5} n^{8} \frac{3}{2}$

Step 3.2

Combine $\frac{m^{5} \cdot 4}{5}$ and $n^{8}$ .

$\frac{m^{5} \cdot 4 n^{8}}{5} \cdot \frac{3}{2}$

Step 4

Combine.

$\frac{m^{5} \cdot 4 n^{8} \cdot 3}{5 \cdot 2}$

Step 5

Cancel the common factor of $4$ and $2$ .

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Step 5.1

Factor $2$ out of $m^{5} \cdot 4 n^{8} \cdot 3$ .

$\frac{2 (m^{5} \cdot 2 n^{8} \cdot 3)}{5 \cdot 2}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $5 \cdot 2$ .

$\frac{2 (m^{5} \cdot 2 n^{8} \cdot 3)}{2 \cdot 5}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (m^{5} \cdot 2 n^{8} \cdot 3)}{2 \cdot 5}$

Step 5.2.3

Rewrite the expression.

$\frac{m^{5} \cdot 2 n^{8} \cdot 3}{5}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $3$ by $2$ .

$\frac{m^{5} \cdot 6 n^{8}}{5}$

Step 6.2

Move $6$ to the left of $m^{5}$ .

$\frac{6 m^{5} n^{8}}{5}$